Train A can cross a man in 8 sec and a 180 m long platform P in 17 sec . If train A cross train B which is running in opposite direction at speed of 108 km/hr in 8 sec , then find time taken by train B to cross platform P ?

Options

A. 16 sec
B. 11 sec
C. 12 sec
D. 14 sec

Answer

C

Explanation

Let the length of train A be L m and speed be V m/s
ATQ -
`V = (L)/(8) " " … (i) `
And , `V = ( L + 180)/(17) " " …. (ii)`
From (i) and (ii)
`(L)/(8) = (L + 180)/(17)`
`17 L - 8 L = 1440`
L = 160 m
And V = 20 m/s
Let length of train B be 'S'
So , `(108)/(18) xx 5 + 20 = (160 + S)/(8)`
S = 400 -160
S = 240 m
Let time taken by train B to cross platform P be t sec
So , `(108)/(18) xx 5 = (240 + 180)/(t)`
`t = (420)/(30) = 14` sec